What is the integral from-1 to 2 of (x^4-2x^3+2) ?

The integral from-1 to 2 of (x^4-2x^3+2) is 51/10

integral from-1 to 2 of (x^4-2x^3+2)

\int_{- 1}^{2} (x^{4} - 2 x^{3} + 2) d x

\frac{51}{10}

Decimal

5.1

Solution steps

\int_{- 1}^{2} x^{4} - 2 x^{3} + 2 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 1}^{2} x^{4} d x - \int_{- 1}^{2} 2 x^{3} d x + \int_{- 1}^{2} 2 d x

\int_{- 1}^{2} x^{4} d x = \frac{33}{5}

\int_{- 1}^{2} 2 x^{3} d x = \frac{15}{2}

\int_{- 1}^{2} 2 d x = 6

= \frac{33}{5} - \frac{15}{2} + 6

Simplify

\frac{33}{5} - \frac{15}{2} + 6 : \frac{51}{10}

= \frac{51}{10}

d er i v a t i v e (7 x + 6)^{3}

\int_{1}^{2} \frac{2}{5} x (x + 1) d x

x \to 15 lim (\frac{x ^{2}}{5} - \frac{3}{x})

\frac{d}{d x} (\frac{x ^{2}}{1 + 2 x})

y^{^{''}} + 16 y = 16 sec (4 t)

What is the integral from-1 to 2 of (x^4-2x^3+2) ?
The integral from-1 to 2 of (x^4-2x^3+2) is 51/10